Question

Se da progresie geometrica. Sa se determine n,daca:
B1=3
Bn=96
Sn=189.

Answer 1

Bn=B1 * q^(n-1)
96 = 3 * q^ (n-1)
32= q^(n-1)
Sn= b1* $\frac {q^{n}-1 }{q-1}$ = b1*$\frac{q^{n-1}*q -1 }{q-1} = b1* \frac{32q-1}{q-1}$
189= 3*$\frac{32q-1}{q-1}$
63*(q-1)=32q-1
63q-32q=63-1
31q=62
q=2
32=2^(n-1)
2^5=2^(n-1)⇒n=6